Someone should be telling your dd that there's no question of her not having contact with her df forever, but because she became so upset while in his care that she self-harmed, called Childline, and was admitted to hospital because of a panic attack, the consensus of opinion of SS, her school, CAHMs etc is that it's in her best interests for contact which involves overnight stays with him to take place when he's got his own home which he has said will be in a month's time and which may enable her to stay with him during the half-term school holiday.. i.e not long for her to wait.
Someone also needs to talk to her about why she became so upset on the Wednesday morning in terms of it being very sad that her dad's girlfriend died and how did this make her feel? Did she feel sorry for dad because he's all alone now? Did she feel sorry for the girlfriend or did she feel glad that she's dead? If she felt that dad's girlfriend was the reason she didn't see him for 11? months, it may be that she wished her dead and believes that her thoughts in some way caused her to die.
It seems to me that your dd needs a lot of reassurance that she doesn't seem to be getting. Children need to know that they're not "bad" for harbouring thoughts that some people regard as being bad and that she shouldn't feel responsible in any way for her dad's girlfriend having died or for him being on his own.
It could be suggested that it would be a nice gesture if she saved her pocket money for a floral or other tribute to be left on the girlfriend's grave or in the garden of memory where she was cremated, and that her dad, or possibly yourself, could take her to pay her respects.
Fwiw, I don't believe the girlfriend died and I'd like to see him squirm what excuses he comes up with when he's asked for her name and where her grave is.